SOLUTION: Two point are given from each of two lines: L1 and L2. Without graphing the points, determine if the lines are parallel, perpendicular, or neither. L1:(3,-2) and (4,8) L2: (1,6)

Algebra ->  Linear-equations -> SOLUTION: Two point are given from each of two lines: L1 and L2. Without graphing the points, determine if the lines are parallel, perpendicular, or neither. L1:(3,-2) and (4,8) L2: (1,6)       Log On


   

Question 212212: Two point are given from each of two lines: L1 and L2. Without graphing the points, determine if the lines are parallel, perpendicular, or neither. L1:(3,-2) and (4,8) L2: (1,6) and (7,-18)
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Two points are given from each of two lines: L1 and L2. Without graphing the points, determine if the lines are parallel, perpendicular, or neither. L1:(3,-2) and (4,8) L2: (1,6) and (7,-18)

Step 1. Need to determine the slopes of L1 and L2. Let m1 be the slope of L1 and m2 be the slope of L2.

Note 1: The lines are perpendicular if the product of the slopes is equal to -1.

Note 2: The lines are parallel if the slopes are equal.

Note 3: And neither if it does not satisfy Notes 1 and 2 above.

Step 2. Slope of Line 1( L1)is given as

m+=+%28y2-y1%29%2F%28x2-x1%29

Given L1:(3,-2) and (4,8), then let y2=8, x2=4, x1=3, y1=-2

m1+=+%288-%28-2%29%29%2F%284-3%29

+m1+=+10%2F1

+m1+=+10

Step 3. Slope of Line 2( L2)is given as

L2: (1,6) and (7,-18), then let x1=1, y1=6, x2=7, and y2=-18


m2+=+%28-18-6%29%2F%287-1%29

+m2+=+-24%2F6

+m2+=+-4

Step 4. The product of m1 and m2 is not equal to -1, so they are not perpendicular.

The slopes are not equal, so they are not parallel.

ANSWER: So the lines are neither perpendicular nor parallel.

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